Markov kernels are a well-studied class of transition kernels.
In this section we use Markov kernels in a novel way as a tool for optimal transport.
[1]} Let \((X,\mathfrak {M})\)  and \((Y, \mathfrak {N})\)  be measurable spaces and \(K\)  a mapping from \(X\times \mathfrak {N}\)  into \([0,\infty ]\) .
Then \(K\)  is called a transition kernel from \((X,\mathfrak {M})\)  into \((Y,\mathfrak {N})\)  if:
